1. Field of the Invention
The present invention relates in general to a femtosecond fiber laser that employs only normal dispersion elements through use of a unique pulse shaping technique. A spectral filter and other non-anomalous dispersion elements are employed in the technique.
2. Description of the Background Art
The need to compensate group-velocity dispersion (GVD) is ubiquitous in femtosecond pulse generation and propagation. Prisms, diffraction gratings and chirped mirrors have all been used to compensate or control GVD. Reliable femtosecond lasers had to await the development of a low-loss means of introducing controllable GVD. Pulse formation in modern femtosecond lasers is dominated by the interplay between nonlinearity and dispersion. In all cases of practical interest, a positive (self-focusing) nonlinearity is balanced by anomalous GVD. The need to compensate normal GVD in the laser, along with the balance of nonlinearity in soliton-like pulse shaping, underlies the presence of anomalous GVD in femtosecond lasers.
Most femtosecond lasers have segments of normal and anomalous GVD, so the cavity consists of a dispersion map, and the net or path-averaged cavity dispersion can be normal or anomalous. With large anomalous GVD, soliton-like pulse shaping produces short pulses with little chirp. Some amplitude modulation is required to stabilize the pulse against the periodic perturbations of the laser resonator. Pulse formation and pulse evolution become more complex as the cavity GVD approaches zero, and then becomes normal. The master-equation treatment of solid-state lasers, based on the assumption of small changes of the pulse as it traverses cavity elements, shows that stable pulses can be formed with net normal GVD. Nonlinear phase accumulation, coupled with normal GVD, chirps the pulse. The resulting spectral broadening is balanced by gain-narrowing. By cutting off the wings of the spectrum, gain dispersion shapes the temporal profile of the chirped pulse. Proctor et al showed that the resulting pulses are long and highly-chirped, as predicted by the analytic theory (B. Proctor, E. Westwig, and F. Wise, “Operation of a Kerr-lens mode-locked Ti:sapphire laser with positive group-velocity dispersion,” Opt. Lett. 18, 1654-1656 (1993)). Stable pulse trains can even be produced without dispersion compensation, but the output pulses are picoseconds in duration and deviate substantially from the Fourier-transform limited duration, even after dechirping with anomalous GVD external to the cavity.
Fiber lasers can be constructed entirely of fiber with anomalous GVD, to generate solitons as short as ˜200 fs in duration. However, the pulse energy is restricted by the soliton area theorem and spectral sidebands to ˜0.1 nJ. Much higher energies are obtained when the laser has segments of normal and anomalous GVD. In general, the pulse breathes (i.e., the pulse duration varies periodically) as it traverses the cavity. Dispersion-managed solitons are observed as the net GVD varies from small and anomalous to small and normal, and selfsimilar and wave-breaking-free pulses are observed with larger normal GVD. The large changes in the pulse as it traverses the laser preclude an accurate analytical treatment, so numerical simulations are employed to study these modes. Among fiber lasers, Yb-based lasers have produced the highest femtosecond-pulse energies, recently reaching 15-20 nJ as reported in Buckley et al. (J. R. Buckley, F. W. Wise, F. O. Ilday, and T. Sosnowski, “Femtosecond fiber lasers with pulse energies above 10 nJ,” Opt. Lett. 30, 1888-1890 (2005)). The normal GVD of single-mode fiber (SMF) around 1 μm wavelength has been compensated by diffraction gratings, which detract from the benefits of the waveguide medium.
With the goal of building integrated fiber lasers, microstructure fibers and fiber Bragg gratings have been implemented to compensate dispersion at 1 μm. However, performance is sacrificed compared to lasers that employ diffraction gratings. Although from a practical point of view it would be highly desirable to design femtosecond-pulse fiber lasers without elements that provide anomalous GVD in the cavity, until now, no known fiber laser can generate ˜100-fs pulses without using anomalous GVD elements.